A Tiny Example

A three-period consumption-savings model with two regimes:

Working life (ages 25 and 45): The agent chooses whether to work and how much to consume. A simple tax-and-transfer system guarantees a consumption floor. Savings earn interest.
Retirement (age 65): Terminal regime. The agent consumes out of remaining wealth.

This notebook teaches the common GridSearch workflow, not a universal model template. If your own model needs EGM, nested EGM, or declared institutional kinks, start from the matching specialized regime and margin declarations. Make the solver-choice checkpoint before adapting the code below.

Model¶

An agent lives for three periods (ages 25, 45, and 65). In the first two periods (working life), the agent chooses whether to work $d_t \in \{0, 1\}$ and how much to consume $c_t$ . In the final period (retirement), the agent consumes out of remaining wealth.

Working life (ages 25 and 45):

V_t(w_t) = \max_{d_t,\, c_t} \left\{ \frac{c_t^{1-\sigma}}{1-\sigma} - \phi \, d_t + \beta \, V_{t+1}(w_{t+1}) \right\}

(1)

subject to

\begin{align} e_t &= d_t \cdot \bar{w} \\[4pt] \tau(e_t, w_t) &= \begin{cases} \theta\,(e_t - \underline{c}) & \text{if } e_t \geq \underline{c} \\ \min(0,\; w_t + e_t - \underline{c}) & \text{otherwise} \end{cases} \\[4pt] a_t &= w_t + e_t - \tau(e_t, w_t) - c_t \\[4pt] w_{t+1} &= (1 + r)\, a_t \\[4pt] a_t &\geq 0 \end{align}

(2)

where $w_t$ is wealth, $e_t$ earnings, $\bar{w}$ the wage, $\underline{c}$ a consumption floor guaranteed by transfers, $\theta$ the tax rate, and $a_t$ end-of-period wealth. The transfer only kicks in when the agent’s resources ( $w_t + e_t$ ) fall below the consumption floor.

Retirement (age 65, terminal):

V_2(w_2) = \max_{c_2 \leq w_2} \frac{c_2^{1-\sigma}}{1-\sigma}

(3)

from pprint import pprint

import jax.numpy as jnp
import numpy as np
import pandas as pd
import plotly.express as px

from lcm import (
    AgeGrid,
    DeterministicTransition,
    DiscreteGrid,
    LinSpacedGrid,
    LogSpacedGrid,
    Model,
    Regime,
    Transition,
    categorical,
)
from lcm.typing import (
    BoolND,
    ContinuousAction,
    ContinuousState,
    DiscreteAction,
    FloatND,
    ScalarInt,
)

Categorical Variables¶

@categorical(ordered=True)
class LaborSupply:
    do_not_work: ScalarInt
    work: ScalarInt


@categorical(ordered=False)
class RegimeId:
    working_life: ScalarInt
    retirement: ScalarInt

Model Functions¶

# Utility


def utility(
    *,
    consumption: ContinuousAction,
    labor_supply: DiscreteAction,
    disutility_of_work: float,
    risk_aversion: float,
) -> FloatND:
    return consumption ** (1 - risk_aversion) / (
        1 - risk_aversion
    ) - disutility_of_work * (labor_supply == LaborSupply.work)


def utility_retirement(*, wealth: ContinuousState, risk_aversion: float) -> FloatND:
    return wealth ** (1 - risk_aversion) / (1 - risk_aversion)


# Auxiliary functions


def earnings(*, labor_supply: DiscreteAction, wage: float) -> FloatND:
    return jnp.where(labor_supply == LaborSupply.work, wage, 0.0)


def taxes_transfers(
    *,
    earnings: FloatND,
    wealth: ContinuousState,
    consumption_floor: float,
    tax_rate: float,
) -> FloatND:
    return jnp.where(
        earnings >= consumption_floor,
        tax_rate * (earnings - consumption_floor),
        jnp.minimum(0.0, wealth + earnings - consumption_floor),
    )


def end_of_period_wealth(
    *,
    wealth: ContinuousState,
    earnings: FloatND,
    taxes_transfers: FloatND,
    consumption: ContinuousAction,
) -> FloatND:
    return wealth + earnings - taxes_transfers - consumption


# State transition


def next_wealth(
    *, end_of_period_wealth: FloatND, interest_rate: float
) -> ContinuousState:
    return (1 + interest_rate) * end_of_period_wealth


# Constraints


def borrowing_constraint_working(end_of_period_wealth: FloatND) -> BoolND:
    return end_of_period_wealth >= 0


# Regime transition


def next_regime(*, age: float, last_working_age: float) -> ScalarInt:
    return jnp.where(
        age >= last_working_age, RegimeId.retirement, RegimeId.working_life
    )

Regimes and Model¶

age_grid = AgeGrid(start=25, inclusive_stop=65, step="20Y")
retirement_age = age_grid.exact_values[-1]

working_life = Regime(
    states={
        "wealth": LinSpacedGrid(start=0, stop=50, n_points=25),
    },
    state_transitions={
        "wealth": next_wealth,
    },
    actions={
        "labor_supply": DiscreteGrid(category_class=LaborSupply),
        "consumption": LogSpacedGrid(start=4, stop=50, n_points=100),
    },
    functions={
        "utility": utility,
        "earnings": earnings,
        "taxes_transfers": taxes_transfers,
        "end_of_period_wealth": end_of_period_wealth,
    },
    constraints={
        "borrowing_constraint_working": borrowing_constraint_working,
    },
)

retirement = Regime(
    states={
        "wealth": LinSpacedGrid(start=0, stop=50, n_points=25),
    },
    functions={"utility": utility_retirement},
)

# At 25 the graph permits both working life and retirement, and the age-based
# `next_regime` selects one; at 45 retirement is the only edge, and `next_regime`
# returns it there. `retirement` has no outgoing edges, which makes it terminal.
edges = {
    "working_life": Transition(
        targets={"working_life": 25, "retirement": (25, 45)},
        law=DeterministicTransition(func=next_regime),
    )
}

model = Model(
    regimes={
        "working_life": working_life,
        "retirement": retirement,
    },
    ages=age_grid,
    edges=edges,
    initial_nodes=((25, "working_life"),),
    regime_id_class=RegimeId,
    description="A tiny three-period consumption-savings model.",
)

Parameters¶

Use model.get_params_template() to see what parameters the model expects, organized by regime and function. The regime-transition law belongs to the edges, so its parameters sit under the "edges" root, keyed by the source regime.

pprint(dict(model.get_params_template()))

{'edges': {'working_life': {'last_working_age': 'float'}},
 'retirement': {'utility': {'risk_aversion': 'float'}},
 'working_life': {'borrowing_constraint_working': {},
                  'certainty_equivalent': {},
                  'earnings': {'wage': 'float'},
                  'end_of_period_wealth': {},
                  'koopmans_aggregator': {'discount_factor': 'FloatND'},
                  'next_wealth': {'interest_rate': 'float'},
                  'taxes_transfers': {'consumption_floor': 'float',
                                      'tax_rate': 'float'},
                  'utility': {'disutility_of_work': 'float',
                              'risk_aversion': 'float'}}}

Parameters shared across regimes (risk_aversion, discount_factor, interest_rate) can be specified at the model level. Parameters unique to one regime go under the regime name. last_working_age, read by the law next_regime, goes under "edges" and the source regime working_life.

params = {
    "discount_factor": 0.95,
    "risk_aversion": 1.5,
    "interest_rate": 0.03,
    "working_life": {
        "utility": {"disutility_of_work": 1.0},
        "earnings": {"wage": 20.0},
        "taxes_transfers": {"consumption_floor": 2.0, "tax_rate": 0.2},
    },
    "edges": {"working_life": {"last_working_age": age_grid.exact_values[-2]}},
}

Simulate¶

n_agents = 100

initial_df = pd.DataFrame(
    {
        "regime_name": "working_life",
        "age": float(age_grid.exact_values[0]),
        "wealth": np.linspace(1, 20, n_agents),
    }
)

result = model.simulate(
    params=params,
    initial_conditions=initial_df,
    log_level="debug",
)

solve call 2312d34928ff phase public_simulate begin

INFO:lcm:solve call 2312d34928ff phase public_simulate begin

solve call 2312d34928ff phase params_validation begin

INFO:lcm:solve call 2312d34928ff phase params_validation begin

solve call 2312d34928ff phase params_validation end status=ok seconds=0.106896

INFO:lcm:solve call 2312d34928ff phase params_validation end status=ok seconds=0.106896

solve call 2312d34928ff phase simulation_inputs begin

INFO:lcm:solve call 2312d34928ff phase simulation_inputs begin

solve call 2312d34928ff phase simulation_inputs end status=ok seconds=0.377009

INFO:lcm:solve call 2312d34928ff phase simulation_inputs end status=ok seconds=0.377009

solve call 2312d34928ff phase authority_fingerprint begin

INFO:lcm:solve call 2312d34928ff phase authority_fingerprint begin

solve call 2312d34928ff phase authority_fingerprint end status=ok seconds=0.004360

INFO:lcm:solve call 2312d34928ff phase authority_fingerprint end status=ok seconds=0.004360

solve call 2312d34928ff phase solver_param_checks begin

INFO:lcm:solve call 2312d34928ff phase solver_param_checks begin

solve call 2312d34928ff phase solver_param_checks end status=ok seconds=0.000046

INFO:lcm:solve call 2312d34928ff phase solver_param_checks end status=ok seconds=0.000046

solve call 2312d34928ff phase state_action_spaces begin

INFO:lcm:solve call 2312d34928ff phase state_action_spaces begin

solve call 2312d34928ff phase state_action_spaces end status=ok seconds=0.000198

INFO:lcm:solve call 2312d34928ff phase state_action_spaces end status=ok seconds=0.000198

solve call 2312d34928ff phase continuation_templates begin

INFO:lcm:solve call 2312d34928ff phase continuation_templates begin

solve call 2312d34928ff phase continuation_templates end status=ok seconds=0.001165

INFO:lcm:solve call 2312d34928ff phase continuation_templates end status=ok seconds=0.001165

solve call 2312d34928ff phase program_graphs begin

INFO:lcm:solve call 2312d34928ff phase program_graphs begin

solve call 2312d34928ff phase program_graphs end status=ok seconds=0.000584

INFO:lcm:solve call 2312d34928ff phase program_graphs end status=ok seconds=0.000584

solve call 2312d34928ff phase structural_resolution begin

INFO:lcm:solve call 2312d34928ff phase structural_resolution begin

structural blueprint: miss (hits=0, misses=1, entries=1)

DEBUG:lcm:structural blueprint: miss (hits=0, misses=1, entries=1)

solve call 2312d34928ff phase structural_resolution end status=ok seconds=0.033923

INFO:lcm:solve call 2312d34928ff phase structural_resolution end status=ok seconds=0.033923

solve call 2312d34928ff phase residency_inventory begin

INFO:lcm:solve call 2312d34928ff phase residency_inventory begin

solve call 2312d34928ff phase residency_inventory end status=ok seconds=0.000007

INFO:lcm:solve call 2312d34928ff phase residency_inventory end status=ok seconds=0.000007

solve call 2312d34928ff phase compilation_waves begin

INFO:lcm:solve call 2312d34928ff phase compilation_waves begin

candidate evaluation ('working_life', 0, 'main') {'action_product': 64, 'cell': 16}

DEBUG:lcm:candidate evaluation ('working_life', 0, 'main') {'action_product': 64, 'cell': 16}

candidate evaluation ('working_life', 1, 'main') {'action_product': 64, 'cell': 16}

DEBUG:lcm:candidate evaluation ('working_life', 1, 'main') {'action_product': 64, 'cell': 16}

candidate evaluation ('retirement', 1, 'main') {'cell': 16}

DEBUG:lcm:candidate evaluation ('retirement', 1, 'main') {'cell': 16}

candidate evaluation ('retirement', 2, 'main') {'cell': 16}

DEBUG:lcm:candidate evaluation ('retirement', 2, 'main') {'cell': 16}

AOT compilation wave 0: 3 unique lowerings for 4 regime-period-core triples (2 workers)

INFO:lcm:AOT compilation wave 0: 3 unique lowerings for 4 regime-period-core triples (2 workers)

1/3  working_life main (age 25, widths={'action_product': 64, 'cell': 16})

INFO:lcm:1/3  working_life main (age 25, widths={'action_product': 64, 'cell': 16})

  lowering working_life main (age 25, widths={'action_product': 64, 'cell': 16}) ...

INFO:lcm:  lowering working_life main (age 25, widths={'action_product': 64, 'cell': 16}) ...

  lowered in 373.7ms

INFO:lcm:  lowered in 373.7ms

  compiling working_life main (age 25, widths={'action_product': 64, 'cell': 16}) ...

INFO:lcm:  compiling working_life main (age 25, widths={'action_product': 64, 'cell': 16}) ...

2/3  working_life main (age 45, widths={'action_product': 64, 'cell': 16})

INFO:lcm:2/3  working_life main (age 45, widths={'action_product': 64, 'cell': 16})

  lowering working_life main (age 45, widths={'action_product': 64, 'cell': 16}) ...

INFO:lcm:  lowering working_life main (age 45, widths={'action_product': 64, 'cell': 16}) ...

  lowered in 293.7ms

INFO:lcm:  lowered in 293.7ms

  compiling working_life main (age 45, widths={'action_product': 64, 'cell': 16}) ...

INFO:lcm:  compiling working_life main (age 45, widths={'action_product': 64, 'cell': 16}) ...

3/3  retirement main (age 45, widths={'cell': 16})

INFO:lcm:3/3  retirement main (age 45, widths={'cell': 16})

  lowering retirement main (age 45, widths={'cell': 16}) ...

INFO:lcm:  lowering retirement main (age 45, widths={'cell': 16}) ...

  lowered in 42.9ms

INFO:lcm:  lowered in 42.9ms

  compiled  working_life main (age 25, widths={'action_product': 64, 'cell': 16})  974.5ms

INFO:lcm:  compiled  working_life main (age 25, widths={'action_product': 64, 'cell': 16})  974.5ms

  compiling retirement main (age 45, widths={'cell': 16}) ...

INFO:lcm:  compiling retirement main (age 45, widths={'cell': 16}) ...

  compiled  retirement main (age 45, widths={'cell': 16})  209.5ms

INFO:lcm:  compiled  retirement main (age 45, widths={'cell': 16})  209.5ms

  compiled  working_life main (age 45, widths={'action_product': 64, 'cell': 16})  907.4ms

INFO:lcm:  compiled  working_life main (age 45, widths={'action_product': 64, 'cell': 16})  907.4ms

AOT compilation wave 0: 3 unique variants compiled, 0 fallback evaluations skipped, 0 fallback requests avoided

INFO:lcm:AOT compilation wave 0: 3 unique variants compiled, 0 fallback evaluations skipped, 0 fallback requests avoided

solve call 2312d34928ff phase compilation_waves end status=ok seconds=1.609609

INFO:lcm:solve call 2312d34928ff phase compilation_waves end status=ok seconds=1.609609

solve call 2312d34928ff phase workspace_selection begin

INFO:lcm:solve call 2312d34928ff phase workspace_selection begin

core plan record {"active_replica_bytes":0,"axis_extents":{"action_product":200,"cell":25},"compiled_collectives":{},"compiler_peak_bytes":971,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"action_product":"streamed","cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":0,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"working_life","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"action_product":64,"cell":16}}

DEBUG:lcm:core plan record {"active_replica_bytes":0,"axis_extents":{"action_product":200,"cell":25},"compiled_collectives":{},"compiler_peak_bytes":971,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"action_product":"streamed","cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":0,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"working_life","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"action_product":64,"cell":16}}

core plan record {"active_replica_bytes":0,"axis_extents":{"action_product":200,"cell":25},"compiled_collectives":{},"compiler_peak_bytes":867,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"action_product":"streamed","cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":1,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"working_life","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"action_product":64,"cell":16}}

DEBUG:lcm:core plan record {"active_replica_bytes":0,"axis_extents":{"action_product":200,"cell":25},"compiled_collectives":{},"compiler_peak_bytes":867,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"action_product":"streamed","cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":1,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"working_life","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"action_product":64,"cell":16}}

core plan record {"active_replica_bytes":0,"axis_extents":{"cell":25},"compiled_collectives":{},"compiler_peak_bytes":236,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":1,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"retirement","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"cell":16}}

DEBUG:lcm:core plan record {"active_replica_bytes":0,"axis_extents":{"cell":25},"compiled_collectives":{},"compiler_peak_bytes":236,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":1,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"retirement","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"cell":16}}

core plan record {"active_replica_bytes":0,"axis_extents":{"cell":25},"compiled_collectives":{},"compiler_peak_bytes":236,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":2,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"retirement","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"cell":16}}

DEBUG:lcm:core plan record {"active_replica_bytes":0,"axis_extents":{"cell":25},"compiled_collectives":{},"compiler_peak_bytes":236,"compiler_reservation_bytes":null,"core":"main","device_ids":[0],"dispatch":{"cell":"streamed"},"logical_gathered_bytes":0,"logical_value_shape":[25],"period":2,"period_transfer_scratch_bytes":{},"physical_value_shape":[25],"regime":"retirement","resident_bytes":null,"selected_block":null,"state_extents":{"wealth":25},"stored_owner_bytes":{},"transfer_workspace_bytes":0,"widths":{"cell":16}}

solve call 2312d34928ff phase workspace_selection end status=ok seconds=0.031951

INFO:lcm:solve call 2312d34928ff phase workspace_selection end status=ok seconds=0.031951

Starting solution

INFO:lcm:Starting solution

solve call 2312d34928ff phase backward_induction begin

INFO:lcm:solve call 2312d34928ff phase backward_induction begin

Age 65 (1 regimes):

INFO:lcm:Age 65 (1 regimes):

  finished in 132.0ms

INFO:lcm:  finished in 132.0ms

Age 45 (2 regimes):

INFO:lcm:Age 45 (2 regimes):

  finished in 26.0ms

INFO:lcm:  finished in 26.0ms

Age 25 (1 regimes):

INFO:lcm:Age 25 (1 regimes):

  finished in 4.6ms

INFO:lcm:  finished in 4.6ms

Inf in V_arr for 1 other state(s) for regime 'retirement', period 2 (age 65.0)

WARNING:lcm:Inf in V_arr for 1 other state(s) for regime 'retirement', period 2 (age 65.0)

Inf in V_arr for 1 other state(s) for regime 'retirement', period 1 (age 45.0)

WARNING:lcm:Inf in V_arr for 1 other state(s) for regime 'retirement', period 1 (age 45.0)

  retirement  age 65.0   V min=-inf  max=-0.283  mean=-inf

DEBUG:lcm:  retirement  age 65.0   V min=-inf  max=-0.283  mean=-inf

  working_life  age 45.0   V min=-2.35  max=-0.774  mean=-1.29

DEBUG:lcm:  working_life  age 45.0   V min=-2.35  max=-0.774  mean=-1.29

  retirement  age 45.0   V min=-inf  max=-0.283  mean=-inf

DEBUG:lcm:  retirement  age 45.0   V min=-inf  max=-0.283  mean=-inf

  working_life  age 25.0   V min=-3.42  max=-1.38  mean=-2.15

DEBUG:lcm:  working_life  age 25.0   V min=-3.42  max=-1.38  mean=-2.15

solve call 2312d34928ff phase backward_induction end status=ok seconds=0.187240

INFO:lcm:solve call 2312d34928ff phase backward_induction end status=ok seconds=0.187240

Solution complete  (188.8ms)

INFO:lcm:Solution complete  (188.8ms)

solve call 2312d34928ff phase result_assembly begin

INFO:lcm:solve call 2312d34928ff phase result_assembly begin

solve call 2312d34928ff phase result_assembly end status=ok seconds=0.003865

INFO:lcm:solve call 2312d34928ff phase result_assembly end status=ok seconds=0.003865

solve call 2312d34928ff phase solution_resolution begin

INFO:lcm:solve call 2312d34928ff phase solution_resolution begin

solve call 2312d34928ff phase solution_resolution end status=ok seconds=0.001703

INFO:lcm:solve call 2312d34928ff phase solution_resolution end status=ok seconds=0.001703

solve call 2312d34928ff phase solution_handover begin

INFO:lcm:solve call 2312d34928ff phase solution_handover begin

solve call 2312d34928ff phase solution_handover end status=ok seconds=0.000004

INFO:lcm:solve call 2312d34928ff phase solution_handover end status=ok seconds=0.000004

solve call 2312d34928ff phase chunk_planning begin

INFO:lcm:solve call 2312d34928ff phase chunk_planning begin

solve call 2312d34928ff phase chunk_planning end status=ok seconds=0.000408

INFO:lcm:solve call 2312d34928ff phase chunk_planning end status=ok seconds=0.000408

solve call 2312d34928ff phase simulation_setup begin

INFO:lcm:solve call 2312d34928ff phase simulation_setup begin

Starting simulation

INFO:lcm:Starting simulation

Simulation plan: route=legacy; 1 cpu device(s) (0,); outer chunks=1 (widths=(100,)); unbudgeted.

INFO:lcm:Simulation plan: route=legacy; 1 cpu device(s) (0,); outer chunks=1 (widths=(100,)); unbudgeted.

Simulation plan detail: route=legacy; subject_devices=(cpu) (0,); axis_widths_by_regime=[working_life: {}; retirement: {}]; outer_chunk_count=1; admitted_chunk_widths=(100,); budget_mode=unbudgeted; effective_device_memory_bytes=None; subject_grouping=None.

DEBUG:lcm:Simulation plan detail: route=legacy; subject_devices=(cpu) (0,); axis_widths_by_regime=[working_life: {}; retirement: {}]; outer_chunk_count=1; admitted_chunk_widths=(100,); budget_mode=unbudgeted; effective_device_memory_bytes=None; subject_grouping=None.

solve call 2312d34928ff phase simulation_setup end status=ok seconds=0.251097

INFO:lcm:solve call 2312d34928ff phase simulation_setup end status=ok seconds=0.251097

solve call 2312d34928ff phase simulation_chunk begin

INFO:lcm:solve call 2312d34928ff phase simulation_chunk begin

Age 25 (1 regimes):

INFO:lcm:Age 25 (1 regimes):

solve call 2312d34928ff phase simulation_compilation begin

INFO:lcm:solve call 2312d34928ff phase simulation_compilation begin

solve call 2312d34928ff phase simulation_compilation end status=ok seconds=0.608833

INFO:lcm:solve call 2312d34928ff phase simulation_compilation end status=ok seconds=0.608833

solve call 2312d34928ff phase simulation_compilation begin

INFO:lcm:solve call 2312d34928ff phase simulation_compilation begin

solve call 2312d34928ff phase simulation_compilation end status=ok seconds=0.046760

INFO:lcm:solve call 2312d34928ff phase simulation_compilation end status=ok seconds=0.046760

solve call 2312d34928ff phase simulation_compilation begin

INFO:lcm:solve call 2312d34928ff phase simulation_compilation begin

solve call 2312d34928ff phase simulation_compilation end status=ok seconds=0.032745

INFO:lcm:solve call 2312d34928ff phase simulation_compilation end status=ok seconds=0.032745

Off-grid next states: regime='working_life', target='retirement', period=0, state='wealth', phase='realized', count=0

INFO:lcm:Off-grid next states: regime='working_life', target='retirement', period=0, state='wealth', phase='realized', count=0

Off-grid next states: regime='working_life', target='working_life', period=0, state='wealth', phase='realized', count=0

INFO:lcm:Off-grid next states: regime='working_life', target='working_life', period=0, state='wealth', phase='realized', count=0

  transitions:
  - working_life → working_life = 100

DEBUG:lcm:  transitions:
  - working_life → working_life = 100

  finished in 2.1s

INFO:lcm:  finished in 2.1s

Age 45 (2 regimes):

INFO:lcm:Age 45 (2 regimes):

solve call 2312d34928ff phase simulation_compilation begin

INFO:lcm:solve call 2312d34928ff phase simulation_compilation begin

solve call 2312d34928ff phase simulation_compilation end status=ok seconds=0.389107

INFO:lcm:solve call 2312d34928ff phase simulation_compilation end status=ok seconds=0.389107

solve call 2312d34928ff phase simulation_compilation begin

INFO:lcm:solve call 2312d34928ff phase simulation_compilation begin

solve call 2312d34928ff phase simulation_compilation end status=ok seconds=0.037626

INFO:lcm:solve call 2312d34928ff phase simulation_compilation end status=ok seconds=0.037626

Off-grid next states: regime='working_life', target='retirement', period=1, state='wealth', phase='realized', count=0

INFO:lcm:Off-grid next states: regime='working_life', target='retirement', period=1, state='wealth', phase='realized', count=0

solve call 2312d34928ff phase simulation_compilation begin

INFO:lcm:solve call 2312d34928ff phase simulation_compilation begin

solve call 2312d34928ff phase simulation_compilation end status=ok seconds=0.043415

INFO:lcm:solve call 2312d34928ff phase simulation_compilation end status=ok seconds=0.043415

  transitions:
  - working_life → retirement = 100

DEBUG:lcm:  transitions:
  - working_life → retirement = 100

  finished in 826.3ms

INFO:lcm:  finished in 826.3ms

Age 65 (1 regimes):

INFO:lcm:Age 65 (1 regimes):

  transitions:
  - retirement → retirement = 100

DEBUG:lcm:  transitions:
  - retirement → retirement = 100

  finished in 66.2ms

INFO:lcm:  finished in 66.2ms

solve call 2312d34928ff phase simulation_chunk end status=ok seconds=3.038752

INFO:lcm:solve call 2312d34928ff phase simulation_chunk end status=ok seconds=3.038752

solve call 2312d34928ff phase simulation_completion begin

INFO:lcm:solve call 2312d34928ff phase simulation_completion begin

Simulation complete  (3.3s)

INFO:lcm:Simulation complete  (3.3s)

solve call 2312d34928ff phase simulation_completion end status=ok seconds=0.000640

INFO:lcm:solve call 2312d34928ff phase simulation_completion end status=ok seconds=0.000640

solve call 2312d34928ff phase simulation_result begin

INFO:lcm:solve call 2312d34928ff phase simulation_result begin

solve call 2312d34928ff phase simulation_result end status=ok seconds=0.006279

INFO:lcm:solve call 2312d34928ff phase simulation_result end status=ok seconds=0.006279

solve call 2312d34928ff phase result_finalization begin

INFO:lcm:solve call 2312d34928ff phase result_finalization begin

solve call 2312d34928ff phase result_finalization end status=ok seconds=0.000009

INFO:lcm:solve call 2312d34928ff phase result_finalization end status=ok seconds=0.000009

solve call 2312d34928ff phase public_simulate end status=ok seconds=5.706592

INFO:lcm:solve call 2312d34928ff phase public_simulate end status=ok seconds=5.706592

df = result.to_dataframe(additional_targets="all")
df["age"] = df["age"].astype(int)
df.loc[df["age"] == retirement_age, "consumption"] = df.loc[
    df["age"] == retirement_age, "wealth"
]
columns = [
    "regime_name",
    "labor_supply",
    "consumption",
    "wealth",
    "earnings",
    "taxes_transfers",
    "end_of_period_wealth",
    "value",
]
df.set_index(["subject_id", "age"])[columns].head(20).style.format(
    precision=1,
    na_rep="",
)

# Classify agents by work pattern across the two working-life periods
first_working_age = age_grid.exact_values[0]
last_working_age = age_grid.exact_values[-2]

df_working = df[df["regime_name"] == "working_life"]
work_by_age = df_working.pivot_table(
    index="subject_id",
    columns="age",
    values="labor_supply",
    aggfunc="first",
)
work_pattern = (
    work_by_age[first_working_age].astype(str)
    + ", "
    + work_by_age[last_working_age].astype(str)
)
assert "work, work" not in work_pattern.to_numpy(), (
    "Plotting assumes that no agent works in both periods of working life."
)

label_map = {
    "work, do_not_work": "low",  # work early, not later
    "do_not_work, work": "medium",  # coast early, work later
    "do_not_work, do_not_work": "high",  # never work
}
groups = work_pattern.map(label_map).rename("initial_wealth")

# Combined descriptives and work decisions table
initial_wealth = df[df["age"] == first_working_age].set_index("subject_id")["wealth"]
group_desc = initial_wealth.groupby(groups).agg(["min", "max"]).round(1)

df_groups = df.copy()
df_groups["initial_wealth"] = df_groups["subject_id"].map(groups)
df_mean = df_groups.groupby(["initial_wealth", "age"], as_index=False).mean(
    numeric_only=True,
)
work_table = df_mean[df_mean["age"] < retirement_age].pivot_table(
    index="initial_wealth",
    columns="age",
    values="earnings",
)
work_table = (work_table > 0).astype(int)
work_table.columns = [f"works {c}" for c in work_table.columns]

summary = pd.concat([group_desc, work_table], axis=1)
summary.index.name = "initial_wealth"
summary.loc[["low", "medium", "high"]].style.format(precision=1, na_rep="")